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Theorem fv2 5536
Description: Alternate definition of function value. Definition 10.11 of [Quine] p. 68. (Contributed by NM, 30-Apr-2004.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) (Revised by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
fv2  |-  ( F `
 A )  = 
U. { x  | 
A. y ( A F y  <->  y  =  x ) }
Distinct variable groups:    x, y, A    x, F, y

Proof of Theorem fv2
StepHypRef Expression
1 df-fv 5279 . 2  |-  ( F `
 A )  =  ( iota y A F y )
2 dfiota2 5236 . 2  |-  ( iota y A F y )  =  U. {
x  |  A. y
( A F y  <-> 
y  =  x ) }
31, 2eqtri 2316 1  |-  ( F `
 A )  = 
U. { x  | 
A. y ( A F y  <->  y  =  x ) }
Colors of variables: wff set class
Syntax hints:    <-> wb 176   A.wal 1530    = wceq 1632   {cab 2282   U.cuni 3843   class class class wbr 4039   iotacio 5233   ` cfv 5271
This theorem is referenced by:  elfv  5539
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-sn 3659  df-uni 3844  df-iota 5235  df-fv 5279
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